4 ms·

It's not immediately obvious to me – why would escape velocity also be the minimum speed at which an object could enter the atmosphere?

digitalsushi 4y ago
Indeed. What if the object was traveling at the same speed as Earth as it revolves around the Sun, and their paths intersect at a very acute angle? That is to say, they met at a traffic 'zipper' ... Could an object collide with earth at a lower speed?
- titzer 4y ago
  Yes, but it is rare because most objects in such orbits tend to either be gobbled by Earth right away, settle into L2, L3, or L4, or enter a high orbit.
- vikingerik 4y ago
  No - because as they approach, Earth's gravitational field accelerates it. Escape velocity is the velocity needed to reach an unbounded height from the surface, so reverse that timewise and any object free-falling towards Earth will have escape velocity upon reaching it.
teraflop 4y ago
Even if an object is moving in a parallel orbit to Earth's around the sun, if you "zoom in" to the point where it enters the Earth's sphere of influence, the influence of the sun is relatively small. It's roughly as if Earth and the object are free-falling together in empty space, with a small relative velocity. And Earth's escape velocity is the same velocity that would be reached by a stationary object "dropped" from infinitely far away. So relative to the Earth it will accelerate and hit the atmosphere with at least escape velocity. (This is only an approximation, but it's a pretty good one because there's such a large difference between Earth's mass and the sun's.) Another way to look at this is to simply observe that Newtonian physics is time-symmetric (neglecting effects like friction that dissipate energy). If you have a trajectory that arrives at the edge of Earth's atmosphere with a certain velocity, you can reverse it to get a trajectory that leaves with the opposite velocity (i.e. equal speed).
vikingerik 4y ago
It's not the minimum possible, but it is the minimum typical case. Escape velocity is the upwards velocity needed at the surface to reach an unbounded height with velocity zero. Run that in the other direction and you see an object that starts from infinity will reach Earth at escape velocity. For that not to happen, you'd need something to perturb the object, slowing its fall or deflecting its velocity in some direction other than down. This can happen from the Moon, but it's not common given its small mass and gravitational field relative to Earth.
VLM 4y ago
Have to hold multiple concepts in head at the same time. If you're "far away" with gravitational potential energy and get "close" to the atmosphere that potential will have to go somewhere and it'll go into speed. Its like how, without a parachute on earth, falling 40 M means about 100 KM/h impact speed. And parachutes don't work outside the atmosphere so its retrorockets or hit pretty fast. Going from up there to down here means a certain velocity on the fall in. Conceptually there is a calculatable difference between the speed "from infinity if the earth were not orbiting the sun" vs "from entering the earth's sphere of influence where the earth gravity matters more than the sun's gravity" but it turns out not to matter much. You're probably going to be coming in very fast from falling into the sun's gravity well. But even if the stars align and you hit the earth's influence at zero m/s (LOL good luck) you'll still hit the atmosphere "around escape velocity" after some rounding.

digitalsushi 4y ago

Indeed. What if the object was traveling at the same speed as Earth as it revolves around the Sun, and their paths intersect at a very acute angle? That is to say, they met at a traffic 'zipper' ... Could an object collide with earth at a lower speed?

titzer 4y ago
Yes, but it is rare because most objects in such orbits tend to either be gobbled by Earth right away, settle into L2, L3, or L4, or enter a high orbit.
vikingerik 4y ago
No - because as they approach, Earth's gravitational field accelerates it. Escape velocity is the velocity needed to reach an unbounded height from the surface, so reverse that timewise and any object free-falling towards Earth will have escape velocity upon reaching it.

teraflop 4y ago

Even if an object is moving in a parallel orbit to Earth's around the sun, if you "zoom in" to the point where it enters the Earth's sphere of influence, the influence of the sun is relatively small. It's roughly as if Earth and the object are free-falling together in empty space, with a small relative velocity. And Earth's escape velocity is the same velocity that would be reached by a stationary object "dropped" from infinitely far away. So relative to the Earth it will accelerate and hit the atmosphere with at least escape velocity. (This is only an approximation, but it's a pretty good one because there's such a large difference between Earth's mass and the sun's.) Another way to look at this is to simply observe that Newtonian physics is time-symmetric (neglecting effects like friction that dissipate energy). If you have a trajectory that arrives at the edge of Earth's atmosphere with a certain velocity, you can reverse it to get a trajectory that leaves with the opposite velocity (i.e. equal speed).

vikingerik 4y ago

It's not the minimum possible, but it is the minimum typical case. Escape velocity is the upwards velocity needed at the surface to reach an unbounded height with velocity zero. Run that in the other direction and you see an object that starts from infinity will reach Earth at escape velocity. For that not to happen, you'd need something to perturb the object, slowing its fall or deflecting its velocity in some direction other than down. This can happen from the Moon, but it's not common given its small mass and gravitational field relative to Earth.

VLM 4y ago

Have to hold multiple concepts in head at the same time. If you're "far away" with gravitational potential energy and get "close" to the atmosphere that potential will have to go somewhere and it'll go into speed. Its like how, without a parachute on earth, falling 40 M means about 100 KM/h impact speed. And parachutes don't work outside the atmosphere so its retrorockets or hit pretty fast. Going from up there to down here means a certain velocity on the fall in. Conceptually there is a calculatable difference between the speed "from infinity if the earth were not orbiting the sun" vs "from entering the earth's sphere of influence where the earth gravity matters more than the sun's gravity" but it turns out not to matter much. You're probably going to be coming in very fast from falling into the sun's gravity well. But even if the stars align and you hit the earth's influence at zero m/s (LOL good luck) you'll still hit the atmosphere "around escape velocity" after some rounding.